In the case of spiral cables, anchoring is known in which the cables are held firmly, in their twisted form, in an anchoring socket by means of a metallic costing material. In the case of parallel-wire and parallel-strand bundles, it it known to spread or bend apart the parallel wires or strands inside an anchoring socket and to anchor them by means of a casting material comprising steel balls and synthetic resin. Another form of anchoring or parallel-wire or parallel-strand bundles is the firm retention of the individual wires or strands in anchoring sockets by wedges. However, these parallel-wire bundles must additionally be held together (banded) over their whole length. A common feature of these known metallic anchoring means is that they fail to withstand varying stress in the area of the base of the cable head or cable anchoring socket, because the casting material is already strained beyond its yield strength under working loads, and friction is thereby produced between the cable or the individual wires or strands and the casting material; with the concommitant action of oxygen, the result is frictional corrosion. In other words, the cable in question tears in the anchored area after a particular number of dynamic stress cycles. The stress amplitudes attainable for two million load cycles with these spiral cable anchors are therefore only about 150 N/mm.sup.2, yet in the areas of use discussed above it is desirable for the permissable stress amplitudes to be approximately 250-300 N/mm.sup.2, in order to be able to fully exploit the cables for static loads. Although in the other known special forms of anchoring of parallel-wire or parallel-strand bundles using steel balls or wedges and a supplementary pouring of resin material, it is possible to attain wider stress ranges, nevertheless these anchorings are very complicated and expensive in terms of both their application and their construction. Furthermore, such parallel-wire and parallel-strand bundles are not sufficiently compact, so provisions for holding the bundle together must be made over its entire length, which again represents increased expense. Still further, resin is not fireproof.